DE112023002220T5 - Machining simulation device and machining simulation method - Google Patents

Abstract

The present disclosure provides a machining simulation apparatus that can obtain a machine tool transfer function without requiring data collection and expert knowledge. The machining simulation apparatus includes: a transfer characteristic generation unit that generates a transfer characteristic of a machine tool; and a simulation execution unit that simulates a behavior of the machine tool using the transfer characteristic. The transfer characteristic generation unit includes: a control information acquisition unit that acquires motor information and a control parameter of a motor control system of the machine tool; a motor characteristic calculation unit that calculates a motor characteristic based on the motor information; a control characteristic calculation unit that calculates a control characteristic of the motor control system based on the control parameter; and a transfer characteristic calculation unit that calculates the transfer characteristic that meets a predetermined requirement based on the motor characteristic and the control characteristic.

Description

Technical area

The present disclosure relates to a machining simulation apparatus and a machining simulation method, and more particularly to a machining simulation apparatus and a machining simulation method for stimulating the behavior of a machine tool using a transfer function representing the transfer characteristic of the machine tool.

State of the art

Techniques for stimulating the behavior of a machine tool and using a transfer function representing the transfer characteristic of the machine tool are disclosed in Patent Documents 1 to 4.

Patent Document 1 discloses a numerical control method that enables machining in a short time without causing damage to the machining surface, even when the command path contains an error. Specifically, Patent Document 1 discloses a numerical control method that predicts a trajectory of a machining tool based on the transfer characteristics from the command position to the machining position in a case where the speed of the machine tool is controlled with the command path and the commanded feedrate specified in the machining program. The method calculates the allowable feedrate based on the characteristic quantities representing the temporal changes in the position of the machining tool along the predicted trajectory and the allowable values thereof. The characteristic quantities include the acceleration or the normal component of the acceleration of the machining tool along the predicted trajectory.

Patent Document 2 discloses a machining simulation device that prevents the occurrence of chatter caused by resonance and improves surface accuracy, etc. Specifically, Patent Document 2 discloses a machining simulation device that performs machining simulation on graphic data before actual machining, simulating the frequency of forced vibration caused by intermittent cutting and/or the frequency of load fluctuations based on machining information using machining simulation means. Based on the frequency obtained from the simulation, a numerical control command is generated by numerical control command generation means. Patent Document 2 also discloses that the machining simulation device allows consideration of the spindle speed in actual machining and in the generation of the machining program under conditions corresponding to actual machining. As a result, the frequency of forced vibrations caused by intermittent cutting and/or the frequency of load fluctuations or harmonic frequencies do not approach the natural vibration frequency of the machine, tool, fixture or workpiece, thus preventing the occurrence of chatter caused by resonance.

Patent Document 3 discloses a processing method that enables the acquisition of correction data in a short time. Specifically, Patent Document 3 discloses a processing method for machining a non-circular workpiece, in which the profile data of the non-circular workpiece is separated into data for the workpiece spindle and the tool feed spindle, and each data set is Fourier transformed. A first step performs Fourier transformation on each data and calculates the gain and phase for each frequency. A second step calculates the gain and phase for each frequency based on the transfer function of the contour machining spindle device and the transfer function of the tool feed spindle device. A third step adds the gain and phase for each frequency obtained in the second step to the gain and phase for each frequency obtained in the first step for the workpiece spindle and the tool feed spindle. A fourth step performs inverse Fourier transformation on the frequency data for the workpiece spindle and the tool feed spindle for the non-circular workpiece obtained in the third step. A fifth step generates correction data, which is the machining data for the workpiece spindle and tool spindle of the non-circular workpiece obtained in the fourth step. Machining of the non-circular workpiece is then performed based on the correction data.

Patent Document 4 discloses a machining simulation device for a machine tool, in which machining simulation can be performed with high accuracy while preventing an increase in time. Specifically, Patent Document 4 discloses a machining simulation device that simulates machining of a workpiece with a machine tool based on a machining program, using the tool to machine the workpiece. The device includes: a machine simulation unit that estimates the position of the tool by simulating the movement of the machine tool based on the position commands and the transmission capabilities of the machine tool when operating in accordance with the machining program; and a machining simulation unit that simulates machining of the workpiece based on the tool information and the estimated position of the tool.

Citation list

patent document

• Patent Document 1: Japanese Unexamined Patent Application Publication No. 2001-051708
• Patent Document 2: PCT International Publication No. WO 2002/003155
• Patent Document 3: Japanese Unexamined Patent Application Publication No. 2002-278609
• Patent Document 4: Japanese Unexamined Patent Application Publication No. 2019-152936

Disclosure of the invention

Problems to be solved by the invention

To perform machining simulation, obtaining the transfer function of a machine tool requires data collection accompanied by trial operation of the machine tool and specialized knowledge to analyze the collected data and calculate the transfer characteristic. Therefore, it is desirable to obtain the transfer function of a machine tool without requiring data collection accompanied by trial operation or specialized knowledge to calculate the transfer characteristic.

Means to solve the problems

A representative first aspect of the present disclosure is a machining simulation apparatus comprising: a transmission characteristic generation unit that generates a transmission characteristic of a machine tool; and a simulation execution unit that simulates a behavior of the machine tool using the transmission characteristic. The transmission characteristic generation unit includes: a control information acquisition unit that acquires control information including motor information of the machine tool and a control parameter of a motor control system of the machine tool from a storage unit; a motor characteristic calculation unit that calculates a motor characteristic based on the motor information; a control characteristic calculation unit that calculates a control characteristic of the motor control system based on the control parameter; and a transmission characteristic calculation unit that calculates the transmission characteristic that meets a predetermined requirement based on the motor characteristic and the control characteristic. The specified requirement includes at least one of a response frequency of a position controller, a response frequency of a speed controller, a natural frequency of the machine tool, or a resonance frequency between a drive unit and a driven unit of the machine tool.

A representative second aspect of the present disclosure is a machining simulation method that causes a computer to perform the following processing: calculating a motor characteristic based on motor information of a machine tool; calculating a control characteristic of a motor control system based on a control parameter of the motor control system of the machine tool; calculating a transfer characteristic that satisfies a predetermined requirement based on the motor characteristic and the control characteristic; and simulating a behavior of the machine tool using the transfer characteristic. The predetermined requirement includes at least one of a response frequency of a position controller, a response frequency of a speed controller, a natural frequency of the machine tool, or a resonance frequency between a drive unit and a driven unit of the machine tool.

Short description of the drawings

• 1 is a configuration drawing illustrating an example of the configuration of a machining simulation system for a machine tool according to an embodiment of the present invention.
• 2 is a drawing showing the drive unit and driven unit of the machine tool using a rigid body model.
• 3 is a drawing illustrating the drive unit and driven unit of a machine tool using a dual inertia system model.
• 4 is a block diagram showing the configuration of a position control loop when the motor control system, the drive unit, and the driven unit form a position control loop.
• 5 is a block diagram illustrating the configuration of a simplified position control loop.
• 6 is a block diagram showing the configuration of a speed control loop when the motor control system, the drive unit, and the driven unit form a speed control loop.
• 7 is a characteristic diagram that represents the frequency response gain of a transfer function.
• 8 is a characteristic diagram showing an example of the frequency response gain of a speed PI control.
• 9 is a characteristic diagram showing an example of the frequency response gain of a speed-P control.
• 10 is a drawing that shows an example of a user interface displayed on a personal computer screen.
• 11 is a flowchart illustrating the operation of the machining simulation device.

Preferred form for carrying out the invention

Hereinafter, an embodiment of the present disclosure will be described in detail with reference to the drawings. 1 is a configuration drawing illustrating an example of the configuration of a machining simulation system for a machine tool according to an embodiment of the present invention.

As in 1 As shown, the machining simulation system 10 for a machine tool includes a machine tool control device 100 and a machining simulation device 200.

The machine tool control device 100 controls the movement of the feed spindle and the rotation of the main shaft of the machine tool based on a machining program. The control device 100 includes a motor serving as a drive unit of the machine tool, a driven unit, and a motor control system that controls the motor. The control device 100 stores motor information of the machine tool and a control parameter of the motor control system in a storage unit 101. The motor information and the control parameter will be described later. The motor information of the machine tool and the control parameter may be stored in a storage unit separate from the control device 100. The storage unit may be provided within the machining simulation device 200. In a case where the storage unit is provided separately from the control device 100, the machining simulation system 10 may not include the machine tool control device 100.

The machining simulation device 200 includes a transfer characteristic generation unit 210 and a simulation execution unit 220. The transfer characteristic generation unit 210 calculates the transfer function of the machine tool using the motor information and the control parameter obtained from the storage unit 101 of the machine tool control device 100. The simulation execution unit 220 uses the calculated transfer function to generate the simulation function generated by the machine tool control device 100 based on the machining program executed control to simulate the behavior of the motor as a drive unit and the driven unit and the control of the control device 100 based on the position information of the drive unit and the driven unit (for example, the position information in 4 shown position control loop described later) and outputs the position information for each shaft as simulation results.

The transfer characteristic generation unit 210 includes a control information acquisition unit 211, a motor characteristic calculation unit 212, a control characteristic calculation unit 213, and a transfer characteristic calculation unit 214. Each configuration of the transfer characteristic generation unit 210 is described below.

(Control information acquisition unit 211)

The control information acquisition unit 211 acquires control information including motor information and a control parameter from the storage unit 101 of the machine tool control device 100. The motor information includes, for example, at least one of a motor inertia, the inertia ratio, or the spring constant, all of which are caused by the motor. The inertia ratio refers to the ratio of the load inertia to the motor inertia. The load inertia is also referred to as load inertia. The motor inertia may also include the inertia of the gear box and the ball screw. The control parameter includes, for example, at least one of the position control proportional gain K _P of the position control unit included in the motor control system of the control device 100, the speed loop gain K _V , the speed control integral gain K ₁ of the speed control unit, or the speed control proportional gain K ₂ of the speed control unit. The storage unit 101 may store the motor inertia as part of the specification or motor characteristic database. In this case, the control information acquisition unit 211 acquires information enabling identification of the motor, such as the motor model, from the storage unit 101 and refers to the specification or motor characteristic database to acquire the motor inertia.

(Engine characteristic calculation unit 212)

The motor characteristic calculation unit 212 calculates a motor characteristic based on motor information. When the mechanical model of the motor serving as the drive unit of the machine tool and the driven unit is 2 , and the motor information includes the motor inertia J _M and the inertia ratio R, the motor characteristic curve M ₁ is given by the transfer function in Equation 1 (hereinafter referred to as "Equation 1"). Here, s represents the Laplace transform. $$M_1\left(s\right)=\frac{1}{\left(1+R\right)J_{M}s}$$

If the mechanical model of the motor, which serves as the driving unit of the machine tool and the driven unit, is represented by the 3 represented by the dual inertia system model shown and the motor information includes the motor inertia J _M , the natural frequency w ₀ and the resonance frequency ω _P , the motor characteristic curve M ₂ is given by the transfer function in Equation 2 (hereinafter referred to as "Equation 2"). $$M_2\left(s\right)=\frac{1}{J_{M}s}\frac{\left(s^2+{\omega }_O{}^2\right)}{\left(s^2+{\omega }_P{}^2\right)}$$

The natural frequency ω ₀ and resonance frequency ω _P in Equation 2 are given by Equation 3 (hereinafter referred to as “Equation 3”) using the motor inertia J _M , the inertia ratio R and the spring constant K _S of the spring element between the motor inertia and the load inertia. $${\omega }_O=\sqrt{\frac{K_S}{R{J}_M},}{\omega }_P=\sqrt{\frac{\left(1+R\right)K_S}{R{J}_M}}$$

The natural frequency ω ₀ of the dual inertia system model is the natural frequency of the free vibration of the driven unit when the drive unit is stationary and can be referred to as the anti-resonance frequency in some cases. The resonant frequency ω _P of the dual inertia system model is the frequency at which the drive unit and the driven unit oscillate in opposite phases.

The transfer function of the motor inertia and load inertia connected by a spring element is disclosed, for example, in: “ A Study on Low Frequency Vibration Suppression Control by Two-Mass System Model for Feed Axes of NC Machine Tools,” Yasusuke Iwashita et al., Journal of the Japan Society for Precision Engineering, Vol. 82, No. 8, 2016 .

(Control characteristic calculation unit 213)

The control characteristic calculation unit 213 calculates the control characteristic of the motor control system based on a control parameter. In a case where the motor control system, the drive unit, and the driven unit included in the control device 100 form a position control loop, the position control loop is controlled by the 4 shown block diagram. As shown in 4 As shown, the position control loop can be represented by a position control unit 111, a speed control unit 112, a mechanical model unit 113 consisting of the drive unit and the driven unit, and an integrator 114. In many cases, the position control loop is configured as a dual-loop system with an inner speed control loop, as shown in 4 is shown. In 4 y' represents the position setpoint, y represents the actual position, r represents the speed setpoint, u represents the manipulated variable, and w represents the actual speed. For example, the manipulated variable u is a torque setpoint; however, for a servo motor, the relationship torque = K _T × current applies via the torque constant K _T , so the manipulated variable u can be considered a current.

Since the response frequency of the position control loop must be lower than the response frequency of the inner velocity control loop, the position control loop can be set to the 4 shown block diagram configuration can be simplified, where the control loop transfer function from the speed command value r to the actual speed w is approximated as 1. In a case where the position control loop is as in 5 As shown, the position control loop consists of the position control unit 111 and the integrator 114, and the motor control system corresponds to the position control unit 111. The control characteristic C _p of the position control unit 111 serving as the motor control system is expressed as C _P = K _P , and the control parameter is the position control proportional gain K _P .

In a case where the engine control system, the drive unit and the driven unit included in the control device 100 form a speed control loop, the speed control loop is controlled by the 6 The speed control loop can be represented by a speed control unit 112 and a mechanical model unit 113 consisting of the drive unit and the driven unit. The motor control system corresponds to the speed control unit 112.

The control characteristic _CV of the speed control unit 112 serving as a motor control system is given by Equation 4 (hereinafter referred to as "Equation 4") in the case of speed PI control. In Equation 4, K _V is the speed loop gain, K ₁ is the speed control integral gain, and K ₂ is the speed control proportional gain. The control parameters are the speed loop gain K _V , the speed control integral gain K ₁ , and the speed control proportional gain K ₂ . $$C_V\left(s\right)=K_V\frac{\left({\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="DE112023002220T5\_0029.png,DE112023002220T5\_0031.png"\; state="\{\{state\}\}">K</figure-callout>}}_1+K_{2}s\right)}{s}$$

In the case of speed-P control, the control characteristic C _V of the speed control unit is obtained by setting K ₁ =0 and K ₂ =1 in Equation 4, resulting in C _V =K _V . The control parameter is the speed loop gain K _V .

(Transfer characteristic calculation unit 214)

The transfer characteristic calculation unit 214 calculates the transfer characteristic of the machine tool by changing at least one of the motor characteristic calculated by the motor characteristic calculation unit 212 or the control characteristic calculated by the control characteristic calculation unit 213 to meet a predetermined requirement. The predetermined requirement includes at least one of the response frequency of the position control, the response frequency of the speed control, the natural frequency of the machine tool, or the resonance frequency between the drive unit and the driven unit of the machine tool. The predetermined requirement will be described later. The value of the predetermined requirement may be provided by the user or may be acquired by the transfer characteristic calculation unit 214 from the storage unit 101 of the control device 100, a storage unit provided outside the control device 100, or a storage unit provided within the machining simulation device.

First, the transfer characteristic of the machine tool is described. The closed-loop transfer function G _C is expressed as G _C = G _O /(1 + G _O ), where G _O is the closed-loop transfer function.

The transfer characteristic calculation unit 214 calculates the closed-loop transfer function G _PC (s) for the position control loop and the closed-loop transfer function G _VC (s) for the velocity control loop as follows. The closed-loop transfer function G _PC (s) for the position control loop, where the open-loop transfer function G _PO (s) of the position control loop is G _PO (s)=K _P /s, as shown in 5 is given by Equation 5 (hereinafter referred to as “Equation 5”). $$G_{PC}\left(s\right)=\frac{G_{PO}\left(s\right)}{\left(1+G_{PO}\left(s\right)\right)}=\frac{K_P}{\left(s+K_P\right)}$$

$$G_{VC}\left(s\right)=\frac{K_V\frac{K_1+K_{2}s}{s}M}{1+K_V\frac{K_1+K_{2}s}{s}M}$$

The closed-loop transfer function G _VC (s) for the velocity control loop in the case of velocity PI control is given by Equation 7 (hereinafter referred to as "Equation 7"), and the open-loop transfer function G _VO (s) is given by Equation 6 (hereinafter referred to as "Equation 6"). In Equations 6 and 7, M represents the motor characteristic curve, where M = M ₁ when the mechanical model is represented by the rigid body system model and M = M ₂ when the mechanical model is represented by the dual inertia system model. $$G_{VO}\left(s\right)=C_V\left(s\right)M=K_V\frac{\left({\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="DE112023002220T5\_0029.png,DE112023002220T5\_0031.png"\; state="\{\{state\}\}">K</figure-callout>}}_1+K_{2}s\right)}{s}M$$

$$G_{VC}\left(s\right)=\frac{{\mathrm{<figure-callout\; id="1"\; label="K\; V\; K"\; filenames="DE112023002220T5\_0029.png,DE112023002220T5\_0031.png"\; state="\{\{state\}\}">K</figure-callout>}}_V\frac{K_{}}{}\frac{{}_1+K_{2}s}{s}\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="DE112023002220T5\_0029.png,DE112023002220T5\_0031.png"\; state="\{\{state\}\}">M</figure-callout>}}{1+{\mathrm{<figure-callout\; id="1"\; label="K\; V\; K"\; filenames="DE112023002220T5\_0029.png,DE112023002220T5\_0031.png"\; state="\{\{state\}\}">K</figure-callout>}}_V\frac{K_{}}{}\frac{{}_1+K_{2}s}{s}M}$$

In the case of velocity-P control, the closed-loop transfer function G _VC (s) for the velocity control loop is obtained by setting K ₁ =0 and K ₂ =1 in Equation 7, resulting in Equation 8 (hereinafter referred to as “Equation 8”). $$G_{VC}\left(s\right)=\frac{K_{\mathrm{<figure-callout\; id="1"\; label="V\; M"\; filenames="DE112023002220T5\_0029.png,DE112023002220T5\_0031.png"\; state="\{\{state\}\}">V</figure-callout>}}M}{1+K_{V}M}$$

Next, the given requirement is described.

(Case where the specified requirement is the frequency response of the position control)

If the transfer function is a rational function of s and the setpoint a is a sine wave with a frequency ω, the controlled variable b also becomes a sine wave with a frequency ω. In this case, the amplitude relationship between the setpoint a and the controlled variable b is called the frequency response gain at the frequency ω. The frequency response gain of the closed-loop transfer function _GC (s) can be calculated by replacing s with jω in Equation 9 (hereinafter referred to as "Equation 9"). The unit is decibel (dB). $$20log\left|G_C\left(j\omega \right)\right|$$

Generally, the frequency response gain of a closed-loop transfer function is close to 0 dB when the frequency response gain of the open-loop transfer function is 0 dB or higher. The case where the frequency response gain of the closed-loop transfer function is close to 0 dB (amplitude ratio of 1) means that the controlled variable b follows the setpoint a. Therefore, the frequency at which the frequency response gain of the closed-loop transfer function crosses 0 dB to -3 dB (amplitude ratio of 1/square root of 2) or becomes a local maximum is called the control response frequency. The frequency at which the frequency response gain of the open-loop transfer function crosses 0 dB is called the control response frequency.

By replacing s with jω in the transfer function G _PC (s) of Equation 5, Equation 10 (hereinafter referred to as “Equation 10”) is obtained and the response frequency ω=K _P becomes the response frequency of the position control, where 20 log |G(jω)| = -3dB. $$\left|G_{PC}\left(j\omega \right)\right|=\frac{K_P}{\sqrt{{\omega }^2+K_P{}^2}}$$

(Case where the specified requirement is the response frequency of the speed control)

When the control characteristic C is the speed-P control and the motor characteristic M is based on the dual inertia system model, the open-loop transfer function of the speed control loop is given by Equation 11 (hereinafter referred to as "Equation 11"). $$G_{VO}\left(s\right)=\frac{K_V}{J_{M}s}\frac{\left(s^2+{\omega }_O{}^2\right)}{\left(s^2+{\omega }_P{}^2\right)}$$

The frequency response gain of the transfer function in equation 11 is 7 schematically represented by the gain diagram. In 7 is the horizontal axis on a logarithmic scale of frequency. The point at which the frequency response gain crosses 0 dB is the response frequency, the point at which the frequency response gain reaches the local minimum is the natural frequency, and the point at which the frequency response gain reaches the local maximum is the resonant frequency.

As in 7 As shown, in general, the relationship between frequencies is as follows: resonance frequency > natural frequency > response frequency of speed control. This relationship also applies to speed PI control. In a case where the frequency ω is not greater than the response frequency of speed control, the relationship is as follows: resonance frequency ω _P > natural frequency ω ₀ > frequency ω (ω _P > ω ₀ > ω), which leads to ω _P ² > ω ₀ ² > ω ² , so the term s ² in Equation 2 can be ignored. By ignoring the term s ^2, Equation 2 becomes equivalent to Equation 1. Therefore, when considering the resonance frequency of speed control, Equation 1 can be used, which represents the rigid body system model as the motor characteristic M.

(Case of speed PI control)

Considering the speed PI control as the control characteristic C and using the rigid body system model as the motor characteristic M, Equation 7 is expressed as Equation 12 (hereinafter referred to as “Equation 12”). $$G_{VC}\left(s\right)=\frac{\left({\mathrm{<figure-callout\; id="1"\; label="K\; V\; K"\; filenames="DE112023002220T5\_0029.png,DE112023002220T5\_0031.png"\; state="\{\{state\}\}">K</figure-callout>}}_V\frac{K_{}}{}\frac{{}_1+K_{2}s}{s}\frac{1}{\left(1+R\right)J_{M}s}\right)}{\left(1+{\mathrm{<figure-callout\; id="1"\; label="K\; V\; K"\; filenames="DE112023002220T5\_0029.png,DE112023002220T5\_0031.png"\; state="\{\{state\}\}">K</figure-callout>}}_V\frac{K_{}}{}\frac{{}_1+K_{2}s}{s}\frac{1}{\left(1+R\right)J_{M}s}\right)}=\frac{K_V{K}_{2}s+K_V{K}_1}{\left(1+R\right)J_M{s}^2+K_V{K}_{2}s+{\mathrm{<figure-callout\; id="1"\; label="K\; V\; K"\; filenames="DE112023002220T5\_0029.png,DE112023002220T5\_0031.png"\; state="\{\{state\}\}">K</figure-callout>}}_V{K}_{}{}_1}$$

By replacing s with jω in Equation 12, Equation 12 is expressed as Equation 13 (hereinafter referred to as “Equation 13”). $$G_{VC}\left(j\omega \right)=\frac{K_V{K}_2\omega j+K_V{K}_1}{K_V{K}_2\omega j+{\mathrm{<figure-callout\; id="1"\; label="K\; V\; K"\; filenames="DE112023002220T5\_0029.png,DE112023002220T5\_0031.png"\; state="\{\{state\}\}">K</figure-callout>}}_V{K}_{}{}_1-\left(1+R\right)J_M{\omega }^2}$$

The frequency response gain is given by Equation 14 (hereinafter referred to as “Equation 14”) using Equation 13. $$\begin{array}{l}20\mathrm{<figure-callout\; id="10"\; label="l\; o\; g"\; filenames="DE112023002220T5\_0031.png,DE112023002220T5\_0032.png"\; state="\{\{state\}\}">l</figure-callout>}o{g}_{}{}_{10}\frac{\left|K_V{K}_2\omega j+{\mathrm{<figure-callout\; id="1"\; label="K\; V\; K"\; filenames="DE112023002220T5\_0029.png,DE112023002220T5\_0031.png"\; state="\{\{state\}\}">K</figure-callout>}}_V{K}_{}{}_1\right|}{\left|K_V{K}_2\omega j+{\mathrm{<figure-callout\; id="1"\; label="K\; V\; K"\; filenames="DE112023002220T5\_0029.png,DE112023002220T5\_0031.png"\; state="\{\{state\}\}">K</figure-callout>}}_V{K}_{}{}_1-\left(1+R\right)J_M{\omega }^2\right|}\\ =10lo{g}_{10}\frac{{\left(K_V{K}_2\omega \right)}^2+{\left(K_V{K}_1\right)}^2}{{\left(K_V{K}_2\omega \right)}^2+{\left[{\mathrm{<figure-callout\; id="1"\; label="K\; V\; K"\; filenames="DE112023002220T5\_0029.png,DE112023002220T5\_0031.png"\; state="\{\{state\}\}">K</figure-callout>}}_V{K}_{}{}_1-\left(1+R\right)J_M{\omega }^2\right]}^2}\end{array}$$

Since in Equation 14, the frequency response gain remains 0 dB or higher up to the values of Equation 15 (hereinafter referred to as "Equation 15") where the magnitudes of the denominator and numerator are equal, the frequency ω of Equation 15 is used as the response frequency of the speed PI control. $$\omega =\sqrt{\frac{2K_V{K}_1}{\left(1+R\right)J_M}}$$

8 is a characteristic diagram showing an example of the frequency response gain for speed PI control.

(Case of speed-P control)

Considering the speed-P control as the control characteristic C and using the rigid body system model as the motor characteristic M, the frequency response gain is obtained by setting K ₁ =0 and K ₂ =1 in Equation 14, resulting in Equation 16 (hereinafter referred to as “Equation 16”). $$20\mathrm{<figure-callout\; id="10"\; label="l\; o\; g"\; filenames="DE112023002220T5\_0031.png,DE112023002220T5\_0032.png"\; state="\{\{state\}\}">l</figure-callout>}o{g}_{}{}_{10}\frac{\left|K_V\omega j\right|}{\left|K_V\omega j-\left(1+R\right)j_M{\omega }^2\right|}=20lo{g}_{10}\frac{K_V}{\left|K_V+j\left(1+R\right)J_M\omega \right|}$$

In Equation 16, the value ω in Equation 17 (hereinafter referred to as “Equation 17”), at which 20 log |G(jω)| = -3dB, is the response frequency of the speed-P control. $$\omega \frac{K_V}{\left(1+R\right)J_M}$$

9 is a characteristic diagram showing an example of the frequency response gain for speed P control.

(Case where the specified requirement is the natural frequency or resonance frequency of the machine tool)

As mentioned above, if the motor which serves as the drive unit of the machine tool and the drive unit is controlled by the 3 represented by the dual inertia system model shown, and the motor information includes the motor inertia J _M , the natural frequency ω ₀ and the resonance frequency ω _P , the motor characteristic curve M ₂ is given by Equation 2. In Equation 2, the natural frequency w ₀ and the resonance frequency ω _P are given by Equation 3 using the motor inertia J _M , the inertia ratio R and the spring constant K _S of the spring element between the motor inertia and the load inertia. The natural frequency w ₀ and the resonance frequency ω _P represent the natural frequency and resonance frequency of the machine tool.

The following describes the method by which the transfer characteristic calculation unit 214 calculates the transfer characteristic of the machine tool to meet the specified requirement. The transfer characteristic generation unit 210 included in the machining simulation device 200 operates as application software on a personal computer and includes the 10 displayed user interface.

10 is a view illustrating an example of a user interface displayed on a display screen of a personal computer. As shown in 10 As shown, the display screen displays the control parameters such as the position control proportional gain K _P , the speed control gain K _V , the speed control integral gain K ₁ and the speed control proportional gain K ₂ , as well as the motor information such as the motor inertia J _M , the inertia ratio R and the spring constant K _S read from the control information acquired by the control information acquisition unit 211. In particular, as shown in 10 As shown, the position control proportional gain K _P is 30, the velocity loop gain K _V is 1, the velocity control integral gain K ₁ is 1089, the velocity control proportional gain K ₂ is 10.164, the motor inertia J _M is 0.022 [kgm ² ], the inertia ratio R is 1.2, and the spring constant K _S is 6878 [Nm], which are displayed on the screen. These control parameters and motor information are changed based on the predetermined requirements entered by the user. On the left side of the screen, an area is displayed in which the user can select the axis for which the model is desired from the multiple axes of the machine tool.

The user specifies the predefined requirement via an input form (not shown). For example, in 10 the result of setting the “Speed control response frequency: Target 50 Hz” is displayed with a dashed line on the graph indicating 50 Hz.

When the user presses the “Apply” button as in 10 As shown, the transfer characteristic calculation unit 214 changes the control characteristic or motor characteristic in accordance with the predetermined requirement and provides the generated transfer characteristic to the simulation execution unit 220. The details of the process for changing the control characteristic or motor characteristic in accordance with the predetermined requirement will be described later.

The display screen shows the frequency response of the open-loop transfer function obtained from the control information reading results. When the user presses the "Apply" button and the transfer characteristic calculation unit 214 modifies the control characteristic or motor characteristic according to the specified requirement and generates the transfer function, the frequency response is updated based on the generated transfer characteristic. Instead of updating the frequency response, the frequency response may be superimposed based on the generated transfer characteristic. Furthermore, the frequency response may also be based on the transfer function _GC (s) that takes feedback into account.

The time at which the transfer characteristic calculation unit 214 changes the control characteristic or motor characteristic or changes the frequency response display need not be when the "Apply" button is pressed and may be the time at which the user changes the specified requirement via the input form.

The 10 The numerical values presented may be rounded to a suitable number of decimal places; however, the number of decimal places has no special meaning and is not specifically limited. 10 Even if the motor inertia is represented as inertia [kgm ² ] assuming a rotary motor, the unit of inertia can be a mass [kg] in the case of a linear motor. Similarly, even if the spring constant is represented as [Nm] assuming a torsion spring, the unit can be [N/m] in the case of a compression spring.

The natural frequency ω ₀ and the resonance frequency ω _P in Equation 3, the frequency ω in Equation 10, the frequency ω in Equation 15, and the frequency ω in Equation 16 are angular frequencies [rad/s]. On the other hand, even if the unit of frequencies is shown in the display screen in 10 and the unit of frequencies represented as given requirements, Hz, shall be rad/s.

The following describes an example of the operation in which the transfer characteristic calculation unit 214 changes the control characteristic or motor characteristic to calculate the transfer characteristic of the machine tool to meet the predetermined requirement.

(1) Example of changing the position control proportional gain K _P to meet the specified requirement of “position control response frequency”

In a case where the user specifies 10 Hz as the response frequency of the position control, the angular frequency for 10 Hz is 10×2π(rad/s)=62.832 (rad/s). As described using Equation 10, since the position control proportional gain K _P is equal to the response frequency of the position control, the position control proportional gain K _P is set to K _P =10×2π=62.832. To meet the specified requirement of the "response frequency of the position control", the position control proportional gain K _P , which is the control characteristic CP, is set from 30 (as in 10 shown) to 62,832.

(2) Example of changing the speed loop gain K _V to meet the specified requirement of “speed control response frequency” (in the case of speed PI control)

The left side of Equation 15 is changed to fc [Hz], resulting in Equation 18 (hereinafter referred to as “Equation 18”). $$f_C=\frac{1}{2\pi }\sqrt{\frac{2K_V{K}_1}{\left(1+R\right)J_M}}$$

In equation 18, the motor inertia J _M remains unchanged. Generally, in PI control, the velocity control integral gain K ₁ and the velocity control proportional gain K ₂ are set in equilibrium; however, here the velocity control integral gain K ₁ remains unchanged. The user can choose to change either the velocity loop gain K _V or the inertia ratio R via a detailed settings option (in 10 not shown). Alternatively, the detailed settings may be configured to prioritize one over the other within the allowable range, and in a case where the specified requirement cannot be met within this range, the other may be changed. The following describes an example in which only the speed loop gain _KV is adjusted to meet the specified requirement of a 50 Hz response frequency for speed control. By solving Equation 18 for the speed loop gain _KV, the speed loop gain _KV is given by Equation 19 (hereinafter referred to as "Equation 19"). $$K_V=\frac{2{\pi }^2{f}_C{}^2\left(1+R\right){\mathrm{<figure-callout\; id="1"\; label="J\; M\; K"\; filenames="DE112023002220T5\_0029.png,DE112023002220T5\_0031.png"\; state="\{\{state\}\}">J</figure-callout>}}_M}{K_{}}=\frac{2{\pi }^2\times {50}^2\times 2.2\times \mathrm{0,022}}{1089}=2.193$$

In this way, in order to meet the specified requirement of “speed control response frequency”, the speed loop gain K _V , which is part of the control characteristic C _V , is changed from 1 to 2.191 and the control characteristic C _V is adjusted accordingly.

(3) Example of changing the speed loop gain K _V to meet the specified requirement of “speed control response frequency” (in the case of speed-P control)

The left side of Equation 17 is changed to fc [Hz], resulting in Equation 20 (hereinafter referred to as “Equation 20”). $$f_C=\frac{K_V}{2\pi \left(1+R\right)J_M}$$

In Equation 20, the motor inertia J _M remains unchanged. This example discusses the case of satisfying the given requirement of "speed control response frequency" (50 Hz) by changing the inertia ratio R. By solving Equation 20 for the inertia ratio R, the inertia ratio R is given by Equation 21 (hereinafter referred to as "Equation 21"). $$R=\frac{K_V}{2\pi J_M{f}_C}-1=\frac{1}{2\pi \times 0.022\times 50}-1=-0.855$$

The inertia ratio R can take a value of 0 in the absence of load inertia, but cannot take negative values. Therefore, assuming R=0 and solving Equation 20 for K _V , the velocity loop gain K _V is given by Equation 22 (hereinafter referred to as "Equation 22"). $$K_V=2\pi f_C{J}_M=2\pi \times 50\times 0.022=6.912$$

In this way, in order to meet the predetermined requirement of “speed control response frequency”, the inertia ratio R of the motor characteristic M ₁ is changed from 1.2 to 0 and the speed loop gain K _V of the control characteristic C _V is changed from 1 to 6.912, thereby changing both the motor characteristic M ₁ and the control characteristic C _V.

(4) Example of changing the spring constant K _S to meet the specified requirement “natural frequency of the machine tool”

By solving equation 3 for the spring constant K _S , the natural frequency w ₀ is given by equation 23 (hereinafter referred to as “equation 23”). $$K_S=R{J}_M{\omega }_O{}^2$$

In a case where the given requirement is a natural frequency of 45 Hz, the spring constant K _S represented in Equation 24 (hereinafter referred to as “Equation 24”) is given by Equation 23. $$K_S=R{J}_M{\omega }_O{}^2=1.2\times 0.022\times {\left(2\times \pi \times 45\right)}^2=2111\left[Nm\right]$$

In this way, in order to meet the specified requirement “natural frequency of the machine tool”, the spring constant K _S of the motor characteristic curve of 6878 [Nm] (as in 10 shown) to 2111 [Nm] and the engine characteristic curve M ₂ is changed accordingly.

(5) Example of changing the spring constant K _S to meet the specified requirement of “resonance frequency between the drive unit and the driven unit of the machine tool”

By solving Equation 3 for the spring constant K _{S ,} the resonance frequency ω _P is given by Equation 25 (hereinafter referred to as “Equation 25”). $$K_S=J_M{\omega }_P{}^2\frac{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="DE112023002220T5\_0029.png,DE112023002220T5\_0031.png"\; state="\{\{state\}\}">R</figure-callout>}}{1+R}$$

In a case where the given requirement is a resonance frequency of 80 Hz, the spring constant K _S represented in Equation 26 (hereinafter referred to as “Equation 26”) is given by Equation 25. $$K_S=J_M{\omega }_P{}^2\frac{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="DE112023002220T5\_0029.png,DE112023002220T5\_0031.png"\; state="\{\{state\}\}">R</figure-callout>}}{1+R}=0.022\times {\left(2\times \pi \times 80\right)}^2\frac{1.2}{2.2}=3032\left[Nm\right]$$

In this way, the spring constant K _S of the motor characteristic curve, in order to meet the specified requirement “resonance frequency of the machine tool”, is set from 6878 [Nm] (as in 10 shown) to 3032 [Nm] and the engine characteristic curve M ₂ is changed accordingly.

In the above examples (4) and (5), the spring constant K _S has been changed; however, the inertia ratio R can be changed instead. The user can choose whether to change either the spring constant K _S or the inertia ratio R via a detailed settings option (in 10 not shown). Alternatively, the detailed settings can be configured to prioritize one over the other within the allowable range, and in a case where the specified requirement cannot be met within that range, the other can be changed.

The transfer characteristic calculation unit 214 may change at least one of the motor inertia, the inertia ratio, the spring constant, the position control proportional gain, the velocity loop gain, the velocity control integral gain, or the velocity control proportional gain so that the transfer characteristic meets the predetermined requirement. In a case where a rigid-body system model that considers the load inertia as the motor characteristic is not used (ie, R=0), the transfer characteristic calculation unit 214 may use a rigid-body system model that adds the load inertia to the motor inertia so that the transfer characteristic meets the predetermined requirement. In a case where a rigid body system model is used as the motor characteristic, the transfer characteristic calculation unit 214 may use a dual inertia system model that combines the motor inertia and the load inertia with a spring element so that the transfer characteristic meets the predetermined requirement.

In the described embodiment, the control characteristic and motor characteristic can be improved by considering more elements, resulting in higher precision in the simulation results. For example, in scientific literature, dampers (for damping) are considered when first deriving the dual inertia system model. Even if the simulation execution unit considers dampers or nonlinearities, dampers or nonlinearities may be ignored when calculating to change a control characteristic or obtain a motor characteristic in the transfer characteristic calculation unit. This is because dampers and nonlinearities are less sensitive to frequency characteristics such as the response frequency, natural frequency, and resonance frequency compared to control gains, inertia ratios, and spring constants.

Each configuration of the machining simulation device 200 has been described above. Next, the machining simulation method will be described. In the following description, the machining simulation method will be described as being performed using the machining simulation device 200; however, the method can also be performed on devices other than the machining simulation device 200.

11 is a flowchart illustrating the operation of the machining simulation device.

In step S1, the control information acquisition unit 211 acquires control information including motor information and a control parameter. The motor information includes at least one of the motor inertia, the inertia ratio, or the spring constant, all of which are caused by the motor. The control parameter includes, for example, at least one of the position control proportional gain K _P of the position control unit, the velocity loop gain K _V , the velocity control integral gain K ₁ of the velocity control unit, or the velocity control proportional gain K ₂ of the velocity control unit, which are included in the motor control system of the control unit 100.

In step S2, the engine characteristic calculation unit 212 calculates the engine characteristic based on the engine information.

In step S3, the control characteristic calculation unit 213 calculates the control characteristic of the engine control system based on the control parameter. Step S3 may be executed before step S2 or may be executed in parallel with step S2.

In step S4, the transfer characteristic calculation unit 214 determines whether the predetermined request has been input. If the request has been input, the process proceeds to step S5; if the request has not been input, the process proceeds to step S6.

In step S5, the transmission characteristic calculation unit 214 changes at least one of the motor characteristic calculated by the motor characteristic calculation unit 212 or the control characteristic calculated by the control characteristic calculation unit 213 to satisfy the predetermined requirement thus inputted.

In step S6, if at least one of the motor characteristics or the control characteristics has been changed in step S5, the transfer characteristic calculation unit 214 calculates the transfer characteristic of the machine tool based on at least one of the thus-changed motor characteristics or control characteristics. If the predetermined request has not been input in step S4, the transfer characteristic calculation unit 214 calculates the transfer characteristic of the machine tool. machine based on at least one of the motor characteristic calculated by the motor characteristic calculation unit 212 or the control characteristic calculated by the control characteristic calculation unit 213.

In step S7, the simulation execution unit 220 uses the calculated transfer function to simulate the control of the machine tool control device 100 based on the machining program, the behavior of the motor as the drive unit and the driven unit, and the feedback control of the control unit 100 based on the position information of the drive unit and the driven unit, and outputs the position information of each shaft as the simulation result.

The components of the machining simulation device described in the above embodiment can be implemented with hardware, software, or a combination thereof. An implementation with software means an implementation with a computer that reads and executes a program. To implement the components of the machining simulation device with software or a combination thereof, the machining simulation device includes a processor, such as a CPU (Central Processing Unit). The processor functions as an execution unit. The machining simulation device may include a plurality of processors operating in parallel. The machining simulation device also includes auxiliary storage devices, such as HDDs (Hard Disk Drives), which store various programs, such as application software or an OS (Operating System), and main storage devices, such as RAM (Random Access Memory), which store the program and data temporarily required for the program during the execution of the functions and operations of the machining simulation device, as shown in the 1 and 6 described. The machining simulation device may include a plurality of main storage devices.

With the machining simulation device, the processor reads the application software or OS from the auxiliary storage device, loads the read application software or OS into the main storage device, and executes a calculation based on the application software or OS. Various hardware components of the machining simulation device are controlled based on the calculation results. In this way, the functional blocks of the present embodiment are implemented.

The components of the machining simulation device can also be implemented in hardware, such as electronic circuits. When the machining simulation device is configured in hardware, some or all of the functions of the machining simulation device components can be implemented in ICs (integrated circuits) such as ASICs (application-specific integrated circuits), gate arrays, FPGAs (field-programmable gate arrays), or CPLDs (complex programmable logic devices).

Programs can be stored and delivered to a computer using various types of non-transitory computer-readable media. Non-transitory computer-readable media encompasses various types of tangible storage media. Examples of non-transitory computer-readable media include magnetic storage media (such as hard disk drives), magneto-optical storage media (such as magneto-optical discs), CD-ROMs (Read Only Memory), CD-Rs, CD-RWs, and semiconductor memories (such as mask ROMs, PROMs (Programmable ROMs), EPROMs (Erasable PROMs), flash ROMs, and RAM (Random Access Memory)). Programs can also be delivered to the computer using various types of transitory computer-readable media.

The effect of the machining simulation apparatus and the machining simulation method as described in the above embodiment is that the transfer function of the machine tool can be obtained without requiring the collection of data during a test operation of the machine tool and without requiring specialized knowledge for calculating the transfer characteristic.

Although the present disclosure has been described above, the present disclosure is not limited to the individual embodiments and modifications described above. Various additions, replacements, modifications, partial deletions, etc. can be made without departing from the scope of the disclosure, as understood from the content of the claims and their equivalents. The embodiments and modifications can also be implemented in combination. For example, the order of operations and the sequence of processing are described as examples in the above embodiments and are not limited thereto.

The following additional notes are further disclosed with respect to the above embodiment:

(Additional note 1)

A machining simulation device (200) comprises: a transmission characteristic generation unit (210) that generates a transmission characteristic of a machine tool; and a simulation execution unit (220) that simulates a behavior of the machine tool using the transmission characteristic, wherein the transmission characteristic generation unit comprises: a control information acquisition unit (211) that acquires control information including motor information of the machine tool and a control parameter of a motor control system of the machine tool from a storage unit; a motor characteristic calculation unit (212) that calculates a motor characteristic based on the motor information; a control characteristic calculation unit (213) that calculates a control characteristic of the motor control system based on the control parameter; and a transfer characteristic calculation unit (214) that calculates the transfer characteristic that satisfies a predetermined requirement based on the motor characteristic and the control characteristic, wherein the predetermined requirement includes at least one of a response frequency of a position control, a response frequency of a speed control, a natural frequency of the machine tool, or a resonance frequency between a drive unit and a driven unit of the machine tool.

(Additional note 2)

The machining simulation device as described in Supplementary Note 1, in which the motor information includes at least one of a motor inertia, an inertia ratio, or a spring constant, all caused by a motor, and the control parameter includes at least one of a position control proportional gain, a speed loop gain, a speed control integral gain, or a speed control proportional gain.

(Additional note 3)

The machining simulation apparatus as described in Supplementary Note 2, in which the motor characteristic calculation unit (212) calculates the motor characteristic using a rigid body system model including the motor inertia and the inertia ratio or a dual inertia system model including the motor inertia, the inertia ratio, and the spring constant.

(Additional note 4)

The machining simulation device as described in Supplementary Note 2, in which the control characteristic calculation unit (213) calculates the control characteristic using the position control proportional gain.

(Additional note 5)

The machining simulation device as described in Supplementary Note 2, in which the control characteristic calculation unit (213) calculates the control characteristic using the speed loop gain or the speed loop gain, the speed control integral gain, and the speed control proportional gain.

(Additional note 6)

The machining simulation device as described in Supplementary Note 1, in which the motor characteristic includes at least one of the motor inertia, an inertia ratio, or a spring constant, the control characteristic includes at least one of a position control proportional gain, a velocity loop gain, a velocity control integral gain, or a velocity control proportional gain, and the transfer characteristic calculation unit (214) changes at least one of the motor inertia, the inertia ratio, the spring constant, the position control proportional gain, the velocity loop gain, the velocity control integral gain, or the velocity control proportional gain so that the transfer characteristic satisfies the predetermined requirement

(Additional note 7)

The machining simulation device as described in Supplementary Note 1, in which the transfer characteristic calculation unit (214) adds a load inertia to the motor inertia, or combines the motor inertia and the load inertia with a spring element, so that the transfer characteristic meets the predetermined requirement.

(Additional note 8)

A machining simulation method that causes a computer to perform processing that includes: calculating a motor characteristic based on motor information of a machine tool; calculating a control characteristic of a motor control system based on a control parameter of the motor control system of the machine tool; calculating a transfer characteristic that satisfies a predetermined requirement based on the motor characteristic and the control characteristic; and simulating a behavior of the machine tool using the transfer characteristic, wherein the predetermined requirement includes at least one of a response frequency of a position control, a response frequency of a speed control, a natural frequency of the machine tool, or a resonance frequency between a drive unit and a driven unit of the machine tool.

Explanation of reference symbols

10

Machining simulation system

100

Machine tool control device

101

storage unit

200

Machining simulation device

210

Transfer characteristic generation unit

211

Control information reference unit

212

Engine characteristic curve calculation unit

213

Control characteristic calculation unit

214

Transfer characteristic calculation unit

220

Simulation execution unit

QUOTES CONTAINED IN THE DESCRIPTION

This list of documents submitted by the applicant was generated automatically and is included solely for the convenience of the reader. This list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited patent literature

• JP 2001-051708 [0006]
• WO 2002/003155 [0006]
• JP 2002-278609 [0006]
• JP 2019-152936 [0006]

Cited non-patent literature

• A Study on Low Frequency Vibration Suppression Control by Two-Mass System Model for Feed Axes of NC Machine Tools,” Yasusuke Iwashita et al., Journal of the Japan Society for Precision Engineering, Vol. 82, No. 8, 2016 [0020]

Claims (8)

A machining simulation device comprising: a transmission characteristic generation unit that generates a transmission characteristic of a machine tool; and a simulation execution unit that simulates a behavior of the machine tool using the transmission characteristic, wherein the transmission characteristic generation unit comprises: a control information acquisition unit that acquires control information including motor information of the machine tool and a control parameter of a motor control system of the machine tool from a storage unit; a motor characteristic calculation unit that calculates a motor characteristic based on the motor information; a control characteristic calculation unit that calculates a control characteristic of the motor control system based on the control parameter; and a transfer characteristic calculation unit that calculates the transfer characteristic that satisfies a predetermined requirement based on the motor characteristic and the control characteristic, wherein the predetermined requirement includes at least one of a response frequency of a position control, a response frequency of a speed control, a natural frequency of the machine tool, or a resonance frequency between a drive unit and a driven unit of the machine tool. The machining simulation device according to Claim 1 wherein the motor information comprises at least one of a motor inertia, an inertia ratio, or a spring constant, all caused by a motor, and the control parameter comprises at least one of a position control proportional gain, a velocity loop gain, a velocity control integral gain, or a velocity control proportional gain. The machining simulation device according to Claim 2 , wherein the motor characteristic calculation unit calculates the motor characteristic using a rigid body system model including the motor inertia and the inertia ratio or a dual inertia system model including the motor inertia, the inertia ratio and the spring constant. The machining simulation device according to Claim 2 , wherein the control characteristic calculation unit calculates the control characteristic using the position control proportional gain. The machining simulation device according to Claim 2 , wherein the control characteristic calculation unit calculates the control characteristic using the speed loop gain or the speed loop gain, the speed control integral gain and the speed control proportional gain. The machining simulation device according to Claim 1 , wherein the motor characteristic includes at least one of the motor inertia, an inertia ratio, or a spring constant, the control characteristic includes at least one of a position control proportional gain, a velocity loop gain, a velocity control integral gain, or a velocity control proportional gain, and the transfer characteristic calculation unit changes at least one of the motor inertia, the inertia ratio, the spring constant, the position control proportional gain, the velocity loop gain, the velocity control integral gain, or the velocity control proportional gain so that the transfer characteristic meets the predetermined requirement. The machining simulation device according to Claim 1 , wherein the transmission characteristic calculation unit adds a load inertia to the motor inertia, or connects the motor inertia and the load inertia with a spring element, so that the transmission characteristic meets the predetermined requirement. Machining simulation method that causes a computer to perform processing that includes: Calculating a motor characteristic based on motor information of a machine tool; calculating a control characteristic of a motor control system based on a control parameter of the motor control system of the machine tool; calculating a transfer characteristic that satisfies a predetermined requirement based on the motor characteristic and the control characteristic; and simulating a behavior of the machine tool using the transfer characteristic, wherein the predetermined requirement includes at least one of a response frequency of a position control, a response frequency of a speed control, a natural frequency of the machine tool, or a resonance frequency between a drive unit and a driven unit of the machine tool.

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